A univalent meromorphic function we defined on Δ:={z ϵℂ:1<|z|<∞} with univalent inverse defined on Δ is bi-univalent meromorphic in Δ. We defined for certain subclasses of meromorphic bi-univalent functions. We obtained estimates on the initial co-efficients. There are many subclasses of analytic and univalent functions. Following the works of Brannan and Taha (1986), Frasin and Aouf (2011) (see also Goodman 1983 and Ma-Minda Bazilevic 1955) on analytic and univalent fumctions, in this paper, we introduce and investigate a new subclass of the function class (formula presented). © Rushing Water Publishers Ltd., Philippines 2017.